Chapter 5.3, Problem 48E

Using Properties of Definite Integrals Given ${\displaystyle {\int }_{-1}^{1}f\left(x\right)dx=0}$ and ${\displaystyle {\int }_0^{1}f\left(x\right)dx=5}$, evaluate

(a) ${\displaystyle {\int }_{-1}^{0}f\left(x\right)dx.}$

(b) ${\displaystyle {\int }_0^{1}f\left(x\right)dx-}{\displaystyle {\int }_{-1}^{0}f\left(x\right)dx.}$

(c) ${\displaystyle {\int }_{-1}^{1}3f\left(x\right)dx.}$

(d) ${\displaystyle {\int }_0^{1}3f\left(x\right)dx.}$